There are a lot of debates about this issue, but morality be a consequence of social interaction does not go so far as to deny the existence of objective morality.
Not a consequence of social interaction, a consequence of social pressure. The pressure to keep the species alive and well.
There is no such thing as "objective morality".
Morality might not exist outside of human relationships, but it is a reality of the human experience, so to us it is an objective fact. Morality is part of the human experience, just like religion.
To us, morality is simply a social pressure and a result of our sociological context. Nothing more. Its not "objective", its in fact completely related to our experience.
Morality differ from one person to another.
For example, for me, you supporting far right bullsh*t is bad, its morally wrong. And yet, for you it's the right thing to do. Morality comes from the the world and our own experience. In that way, it can't be objective.
What is important in reality is not morality. What are important are the facts:
Is it morally bad to support far right ideas ? Depending on the person, not necessarily.
But
Are far right ideas bad for the wellbeing of humankind ? Objectively yes.
That's why I do not look at morality but I always look at the facts and their impact on society to tell you that you are bigoted.